Different Zhang functions leading to different ZNN models illustrated via time-varying matrix square roots finding

0957-4174/$ see front matter 2013 Elsevier Ltd. A http://dx.doi.org/10.1016/j.eswa.2013.01.045 ⇑ Corresponding author. Tel.: +86 13060687155. E-mail addresses: [email protected], ynzh In view of the great potential in parallel processing and ready implementation via hardware, neural networks are now often employed to solve online nonlinear matrix equation problems. Recently, a novel class of neural networks, termed Zhang neural network (ZNN), has been formally proposed by Zhang et al. for solving online time-varying problems. Such a neural-dynamic system is elegantly designed by defining an indefinite matrix-valued error-monitoring function, which is called Zhang function (ZF). The dynamical system is then cast in the form of a first-order differential equation by using matrix notation. In this paper, different indefinite ZFs, which lead to different ZNN models, are proposed and developed as the error-monitoring functions for time-varying matrix square roots finding. Towards the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, the MATLAB Simulink modeling and verifications of such ZNN models are further investigated for online solution of time-varying matrix square roots. Both theoretical analysis and modeling results substantiate the efficacy of the proposed ZNN models for time-varying matrix square roots finding. 2013 Elsevier Ltd. All rights reserved.